**Campus Recruitment – Logical Reasoning – **Arithmetic Reasoning

Contents

**Concepts**

Arithmetic Reasoning involves logical calculation, Venn-diagram and data-based problems. In this type of problems, some information is given, which makes us get confused. You need to analyze that information carefully and answer the question accordingly.

**Conceptual Examples**

1) Kiran, an eight years old boy has 27 toys. He gave 19 toys to his brother Gourav, while Gourav playing all but 6 got destroyed. While Kiran playing all but 3 got destroyed. Finally how many toys left with both of them?

a) 10 b) 18 c) 9 d) 8 e) none of these

**Explanation**: While Gourav playing ‘All but 6 got destroyed’ means ‘All except 6 got destroyed’. i.e., 13 toys got destroyed. It means now Gourav has 6 toys. While Kiran is playing ‘All but 3 got destroyed’ means ‘except 3 all are not working i.e; 3 toys are good working so total toys at both of them is 6 + 3 = 9.

2) Rohith,who works in a parcel service, has a certain number of small plastic boxes to pack into parcels. If he packs 3,4,5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcel, none is left over. What is the number of boxes, he may have to pack?

a) 300 b) 500 c) 301 d) 200 e) 201

**Explanation**: The required number of boxes is such that it leaves a remainder of 1 when divided by 3, 4, 5 or 6 and no remainder of 1 when divided by 3, 4, 5 or 6 and no remainder when divided by 7. Such a number is 301.

3) If man pays RS 20 for each km which he travels by taxi and RS 10 for each km which he travels by bus. If in one week he payed RS 800 for traveling 60 km. How many kilometers did he travel by taxi ?

a) 10 b) 15 c) 25 d) 20 e) 50

**Explanation**: Let the distance covered by the taxi be ‘x’ km. Then, distance covered by bus = (60 -x) km.

20x +10 (60 – x)=>20x + 600 – lOx = 800

lOx = 200 => x = 20 km.

He traveled 20 km by taxi.

4) In a group of dogs and peacocks, the number of legs are 18 less than four times the number of heads How many peacocks are there in that group?

a) 9 b) 16 c) 8 d) 12 e) 13

**Explanation**: Let the number of dogs be ‘x’ and the number of peacocks by ‘y’. ,

Then, number of legs in the group = 4x + 2y.

Number of heads in the group = x+y

So, 4x+2y – 4 {x+y) -18 => 2y = 18 => y = 9

Number of peacocks in that group = 9.

5) In a group of 15 people, 8 read English, 7 read French while 3 of them read none of these two. How many of them read French and English both?

a) 6 b) 3 c) 5 d) 4 e) 2

**Explanation**: In the following Verm diagram, F and E represent people who read French and English respectively.

Now, [F+({F ∩ E}) + E] = 15-3 (or) F+E+(F ∩ E) = 12…. (1)

Also, F+(F ∩ E) = 7; E+(F ∩ E) = 8.

By adding, F+E+2(F ∩ E) = 15 …. (2)

By subtracting (1) from (2), we get (F ∩ E) = 3.

3 of them read both French and English.

**Exercise **

1) The number of girls in a class is 5 times the number of boys. Which one of the following numbers cannot represent the total number of children in the class.

a) 36 b) 41 c) 42 d) 48 e) 72

2) In a class, there are 21 boys who are over 160 cm tall. If these constitute three-fourth of the boys and the total number of boys is one-fourth of the total number of students in the class. What is the total number of girls in the class?

a) 84 b) 68 c) 74

d) 64 e) cannot be determined

3) In a BCCI meeting there are ten people. All shake hands with each other once. How many handshakes will be there altogether?

a) 10 b) 100 c) 45 d) 95 e) 15

4) A certain number of donkeys and an equal number of men are going to a village. Half of the men are on their donkey’s back while the remaining are walking along leading their donkeys. If the number of legs walking on the ground is 70. How many donkeys are there?

a) 16 b) 18 c) 17 d) 14 e) 28

5) A group of 1800 persons consists of captains and players is traveling in a train. For every 17 players there is one captain. The number of captains in the group is?

a) 105 b) 106 c) 100 d) 104 e) 107

6) When Rahul was bom, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rahul’s brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul’s sister when he was bom?

a) 20 years b) 35 years c) 25 years d) 45 years e) 10 years

7) Five friends Akhil, Nikil, Charan, Sudha, Shyamala, playing a game of chocolates. Akhil says to Nikil, “If you give me 3 chocolates, you will have as many as I have at this moment” while if Sudha takes 5 chocolates from you, she will have as many as Shyamala has. Akhil and Charan together has twice as many chocolates as Shyamala has. Also Nikil and Sudha together have the same number of chocolates as Akhil and Charan taken together. If together they have 150 chocolates, how many chocolates does Charan has?

a) 28 b) 30 c) 32 d) 34 e) 36

8) Spriha has few sweets to be distributed. If she keep 2, 3 or 4 in a pack, she is left with one sweet. If she keep 5 in a pack, she is left with none. What is the minimum number of sweets she has to pack and distribute?

a) 21 b) 25 c) 37 d) 54 e) 65

9) A bus starts from city x. Total number of men in the bus is half of the number of women. In city y, 10 women leave the bus and five men enter. Now, number of women and men are equal. In the beginning, how many passengers entered the bus?

a) 45 b) 35 c) 36 d) 34 e) 46

10) Jhansi cut a cake in to two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is 25 gram is weight. If she has eight pieces of the cake in all with her, what is the weight of the original cake?

a) 405 grams b) 305 grams c) 400 grams d) 450 grams e) 350 grams

11) A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 12 pieces. He cut at the rate of 44 cuts a minute. How many rolls would be cut in 26 minutes?

a) 100 rolls b) 102 rolls c) 103 rolls

d) 104 rolls e) none

12) P is 3 years older to Q and 3 years younger to R. while Q and S are twins, how many years older is R over S?

a) 3 years b) 5 years c) 6 years d) 8 years e) 4 years

13) A monkey climbs 40 feet at the beginning of each hour and rests for a while. It slips back 30 feet before it again starts climbing. If it begins climbing at 9:00 am, at what time will it first touch a flag at 130 feet high from the ground?

a) 5 pm b) 6 pm c) 7 pm d) 8 pm e) None

14) Between two books in your study room are displayed your six favorite puzzle books. If you decide to arrange the six books in every possible combination and moved just one book every minute, how long would it take you?

a) 6hours b)2 hours c)10 hours d)12hours e)None

15) A man wears socks of two colors named black and white. He has altogether 30 black socks and 30 white socks in a drawer. Suppose he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?

a) 20 b) 3 c) 4 d) 39 e) 30

16) A farmer built a fence around his square plot. He used 28 fence poles on each side of the square. How many poles did he need altogether?

a) 104 b) 112 c) 108 d) 100 e) 114

17) A businessman earns an income of Rs 2 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of business, his income is how much?

a) 1000 b) 1004 c) 1024 d) 1204 e) 1402

18) The 24 members of a club decided to play a badminton singles tournament. A member will be out of tournament if he loses a game. There are no ties. What is the minimum number of matches that must be played to determine the winner?

a) 11 b) 23 c) 16 d) 12 e) 20

19) A man has Rs 1400 in the “denominations of five, ten and twenty rupee notes. The number of each denomination is equal. What is the total number of notes that he has?

a) 120 b) 130 c) 140 d) 150 e) 160

20) In a hall in addition to 60 hens, there are 50 sheep and 10 horses with some keepers. If the total number of feet be 260 more than the number of heads in the hall, the number of keepers is?

a) 10 b) 8 c) 120 d) 20 e) Cannot be determined

21) Two Train tickets from city A to B and three tickets from city A to C cost Rs 65 but three tickets from city A to B and two tickets from city A to C costs Rs 70. What are the fares for cities B and C from A?

a) Rs 1o, Rs 12 b) Rs 16, Rs 11 c) Rs 13, Rs 14

d) Rs 15, Rs 12 e) Cannot be determined

22) An institute organized a fete and 1/6 of the girls and 1/7 of the boys participated in the same. What fraction of the total number of students took part in the fete?

a) 2/13 b) 13/42 c) Data inadequate

d) 4/32 e) None of these

23) A mango costs Rs 7 each. An orange costs Rs 5 each. Vinod spends Rs 38 on these two fruits. The number of Mangoes purchased is?

a) 2 b) 3 c) 4

d) Data Inadequate e) None of these

24) What is the product of all the numbers in the dial of a telephone?

a) 168840 b) 178480 c)169480

d) None of these e) Cannot be determined

25) What is the smallest number of cows that could walk in this formation – two cows in front of a cow, 2 cows behind a cow and a cow between two cows?

a) 3 b) 4 c) 8 d) Cannot be determined e) 100

26) Abhiram got twice as many sums wrong as he got right. If he attempted 54 sums in all, how many did he solve correctly?

a) 16 b) 14 c) 18 d) 24 e) 2027

27) If every 2 out of 3 ready made shirts need alterations in the sleeves, 3 out of 4 needs alterations in collars and every 4 out of 5 need it in the body, how many alterations will be required for 60 shirts?

a) 133 b) 60 c) 120 d) 14 e) 170

28) A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their place. What is the number?

a) 37 b) 30 c) 47 d) 50 e) 67

29) A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages the book have?

a) 2000 b) 300 c) 1074 d) 1075 e) 2001

30) First bunch has 1/4 more bananas as a second 4 bunch. If the second bunch has 3 bananas less than the first bunch, then the number of bananas in the first bunch is.

a) 14 b) 15 c) 16 d) 17 e) 18

31) A man asked a hunter that how many birds he has in the bag. He replied that there were all pigeons but eight, all Nightingales but eight, and all ducks but eight. How many birds had he in all?

a) 9 b) 10 c) 12 d) 14 e) 16

32) A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son is?

a) 15 b) 20 c) 25 d)30 e)35

Directions (33-35): The diagram given below shows the number of students who got distinction in three subjects out of 500 students. Study the diagram carefully and answer the questions that follow.

33) What is the percentage of students who got distinction in two subject?

a) 12% b) 14% c) 10% d) 16% e) 15.4%

34) What is the percentage of students who got distinction?

a) 44% b) 64% c) 53.48% d) 63.48% e) 74%

35) The percentage of students with distinction marks in Mathematics is?

a) 22.63% b) 21.63% c) 32.63% d)21.6% e) 24.6%

**Explanations**

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